Well-posedness and stability of nonlinear wave equations with two boundary time-varying delays

  • Salah Zitouni
  • Abdelouaheb Ardjouni
  • Mouataz Billah Mesmouli
  • Rachida Amiar

Abstract

In this paper, we consider a nonlinear wave equation with two time-varying delays term in the boundary condition in a bounded domain $\mathbb{R}^{n}$ a boundary $\Gamma $ of class $C^{2}$ such that $\Gamma =\Gamma
_{D}\cup \Gamma _{N}$, with $\overline{\Gamma _{D}}\cup \overline{\Gamma _{N}}=\emptyset $, $\Gamma _{D}\neq \emptyset $ and $\Gamma _{N}\neq \emptyset $. Well-posedness of the problems is analyzed by using semigroup theory. The
exponential stability of the problem is proved.

Published
2017-05-26